Simplify (2x^4y^4)^3

${(2 x^{4} y^{4})}^{3}$

Step 1

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $2 x^{4} y^{4}$ .

${(2 x^{4})}^{3} {(y^{4})}^{3}$

Apply the product rule to $2 x^{4}$ .

$2^{3} {(x^{4})}^{3} {(y^{4})}^{3}$

Step 2

Raise $2$ to the power of $3$ .

$8 {(x^{4})}^{3} {(y^{4})}^{3}$

Step 3

Multiply the exponents in ${(x^{4})}^{3}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$8 x^{4 \cdot 3} {(y^{4})}^{3}$

Multiply $4$ by $3$ .

$8 x^{12} {(y^{4})}^{3}$

Step 4

Multiply the exponents in ${(y^{4})}^{3}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$8 x^{12} y^{4 \cdot 3}$

Multiply $4$ by $3$ .

$8 x^{12} y^{12}$